Electromagnetic horn



April 3- W. L. BARROW I 2,316,151

ELECTROMQGNE'IIC HORN Filed Jan. 9, 19:9 2 s eets-sues; 1

, lNVENTOi? W M L. B ROW Ev ATTORNEY ELECTROMAGNETIC HORN Filed Jan. 9, 1939 a 2 Sheets-Sheet 2 Q 63 3:3: 55/ 3 L; I g i ATTORNEY Patented Apr. 13, 1943 h 2,316,151 ELECTROMAGNETIC HORN Wilmer Lanier Barrow, Newton, Mass., assignor to Research Co ration, New York, N. corporation of New York Application January 9, 1939, Serial. No. 249,910

. 20 Claims.

' The present invention relates to electromagnetic horns. r

To avoid ci'rcumlocution of language, when the vliornis recited in the claims as having exciting or absorbing means}? it will be understood generically that either the horn is provided with either an exciting or absorbing antenna or the like, or else that a hollow-pipe transmission system or the like is connected to the throat of the horn. When exciting or absorbing" is recited in the claims as positioned in the throat of the horn, it will be understood that an exciting or absorbing antenna or the like is positioned in the throat of the horn.

It is by no means true that any horn will transmit or receive any wave, and an object of the present invention is to assure the production near the mouth of the horn of a wave of a desired type, such as the Hm or H1,o wave.

Onthe other'hand, a plurality of diflzerent types of horn waves may be generated, depending upon the configuration of the exciting means in the throat of the horn, or upon the nature of thewaves delivered there by a hollow-pipe transmission system, and also upon the flare angle 60 and the cut-ofl length pc from the apex tothe throat, or small or reflecting end, or the back of the horn. Special cases may arise wherein several wave-types may be used simultaneously;

In many applications, however, a single waveshould obtain near the mouth of the horn, as the radiation'pattern will be distorted by the presence of other waves.

A .further object, therefore, is to exclude waves of other types than those desired. To the attainment of these ends,'it is desirable to position the exciting or absorbing means properly, or properly to design the size of the throat and the radial length of the horn, or both.

. Another object is to provide a horn having a predetermined performance.

' A further object is to provide quantitative curves to facilitate the design of such horns.

Other and further objects will be explained hereinafter and will be particularly pointed out in the appended claims.

The invention will now be described in connection with the accompanying drawings, in which Fig. 1 is a perspective, partly broken away, of a sectoral electromagnetic horn embodying the invention, and fed by a hollow-pipe line;

Figs. 2 and 3 are similar perspectives of modifications;

Fig. 4 is a diagrammatic'perspective of a sectoral horn, disposed in Cartesian and cylindrical systems of co-ordinates, and carrying symbols useful in describing the invention;

Fig. 5 is a plot of two curves showing the relation between the flare angle or: and the cut-oil length p0 of the horn from the apex to the throat, the cut-oil length po being of the wave length A;

Figs. 6 and 7 are plots of further curves to be described more fully hereinafter; and

Figs. 8 and 9 are views similar to Figs. 1 and 4, respectively, of a conical horn.

In Figs. 1 to 4, there is illustrated a horn it of rectangular cross section, flaring smoothly and continuously from the throat to a mouth or aperture or. large end of the horn, at its front. The principal or central axis of, the horn extends between the smaller and larger ends of the horn. At its throat, it is shown connected to a hollowpipe transmission system comprising an elongated hollow pipe or tube body portion or section. i8 that'is connected to the throat of the horn so as to extend over any desired distance from the horn, to the left, as viewed in Figs. 1 to 4.

The horn may be constituted of aformed sheet of conducting material, like. metal, such as cop per or aluminum, or it may b constituted of other material if its inner wall is otherwise rendered a conductor of the saidwaves. The hollowpipe body portion It, to which the horn lt is connected,'may be of any desired material, conducting or dielectric, or it may otherwise be provided with an inner conducting wall. It may contain air or other gas, or it may be evacuated. If the body portion 18 is constituted of a metal pipe, the flared-out continuation may constitute a conducting extension of the body portion 18.

If the horn I6 is of simple rectangular shape, the pipe portion i 8, from which it flares out. may

be likewise rectangular. The horn may, however, have abrupt changes. Screen or other semi-open construction may also be employed. As dielectric supports and insulators are not required in represented in terms to sides of varying flare, such as exponential or hyperbolic.

' The waves inside these horns, at a distance several wave-lengths from the throat, are governed, among other things, by the dimensions of the sides and the flare angle 1/.

The horn of the present invention may be useo for transmission or reception of ultra-hilgh-irequency electromagnetic waves. In transmission,

electromagnetic energy, transmitted through the interior of the pipe or tube II from a projecting metal exciting or absorbing antenna rod or other energy-translating apparatus II, is delivered to the throat of the horn and propagated through the interior of the horn to the mouth'as horn waves." At the mouth, substantially all of this energy is radiated. into free space as ordinary radio waves. The horn thus constitutes a directive electromagnetic radiator.

In receiving, a similar, but reverse, process takes place, the electromagnetic waves being received by the horn l8, and communicated to a receiving system (not shown).

The rod II is shown in Fig. 1 disposed approximately centrally in the hollow pipe i8, substantially at right angles to the axis of the horn, but it may be disposed unsymmetrically in the horn, to give a modified directive pattern for the radiant energy.

Sending apparatus (not shown) may be connected to a coaxial-line system I0, i2, or to a. parallel-wire system, or to any other desired connecting system. The conductor 12 may be extended into the bell of the horn or the tube i8,

.either parallel to the top and bottom walls, as

in Fig. 3, or at right angles thereto, as in Figs. 1 and 2, to constitute the antenna I4.

Diflerent types of horn waves, and combinations of the same, may be separately excited and propagated within the hom, or absorbed by the hom, by properly arranging the exciting rod or rods in or out of the throat of the horn, both as to the position of, and the current in, the rod or rods.

One of the most important modes or wave types is the lowest-order transversely polarized horn wave I-Io,1, with the electric vector mainly parallel everywhere to the vertical direction, obtained with an exciting rod I4 transverse to the axi and in the vertical plane. Another important mode or wave type is the Hm wave. These two wave types are probably the best for sending a single I beam of radiant energy and are the waves most naturally adopted for receiving. For beam transmission, a horn of rectangular cross section perpendicular to its principal or central axis, and

secondary lobes. For this reason, the use oisectoral horns is particularly advantageous in certain kindsof applications where the shape of the beam plays an essential role in the operation.

the orientation of the exciting rod perpendicular to this axis, offer certain features, among them the important feature of a radiated linearly polarized space wave. The rectangular shape, furthermore, permits independent control of the width of the radiated beam in the horizontal and vertical planes.

Beams transmitted from directive antenna systerns are usually accompanied by small amounts of radiation in directions other than those intended. These small amounts of radiation are referred'to as secondary lobes. Beam radiated rom sectoral horns may be remarkably free from In the blind-landing of airplanes, for example, it is-desirable, not only that the beam be very sharp, but also that it be peculiarly free from secondary lobes. In one such application, a smooth straight-line intersection is formed between two overlapping beams; systems of this type are commonly referred to as "equal-signal" systems. Horn radiators can provide such smooth overlapping beams without waviness or spurious components that would aflect the straightness of this path of intersection. No other types of antenna have been found to produce so smooth beams with such small secondary lobes. Patterns of this character are useful also in other applications, such as direction-finding and obstacle-detection.

' Though the analysis in connection with sectoral horns, it applies also very approximately to horns that are somewhat pyramidal in which the two substantially parallel sides are not strictly parallel but diverge to some extent. The term substantially sectoral" will be employed in the claims to include somewhat pyramidal horns of this nature.

In Figs. 1 and 3, as before described, the horn i6 is shown excited by means of a hollow-pipe transmission line It, connected to the throat of the horn, with the translating apparatus positioned in the pipe It, at the rear of the throat of the horn; The antenna then first excites waves in the hollow pipe, which are transmitted times desirable, however, as explained in my application, Serial No. 240,545, filed November 15, 1938, that the translating apparatus be positioned directly in the throat of the horn, as illustrated in Fig. 2, in order directly to excite the horn itself, without the use of a hollow-pipe transmission line. It then operates efiiciently to receive substantially all of' the incident energy, when used as a receiver; or, when used as a transmitter, to excite waves of the horn type, and thereby to radiate a beam of character appropriate to the horn rather than to the apparatus and the antenna itself, With the apparatus in the throat,

furthermore, the horn has smaller physical diergy-translating means directly in the throat of the horn, is applicable to longer waves. Substantially the same radiation pattern may be produced with either arrangement.

The invention is not, of course, limited to the use of an exciting or absorbing rod l4. Other radiating or absorbing means, such as a vacuum tube, may also be employed, as described, for example, in the said application, Serial No. 240,545, filed November 15, 1938. As is also explained in the said application, Serial No. 240,545, optimum conditions may be obtained by adjusting a piston (not shown) at the back or throat of the horn, thus to resonate or tune the throat of the horn, thereby rendering the throat of the horn more responsive to a particular frequency or a narrow band of frequencies than to other fre quencies, and also in other ways.

will be hereinafter given 1 I wilijbe this spJ, cation will-be understood by reference to Fig. 4. The

lower of the two parallel sides oi the horn oi .Flg. f1 is'here assumed to lie in the XZ plane, with its non-parallel or flaring sides,extend'ed, intersect:

ing on, and making equal. angles with, the Y .{scripts eachrepresenting a positive integer'denoting the number of halt-sinusoidal variations 'infthe' field between-the top axis. The system maybe regarded as symbolf 'i'zing also cylindrical co-ordinates ii, p and o. .The'

upper parallel side oi the hornis parallel to the X2 plane, and at at distance a therefrom. It is assumed that the throat of the horn is disposed along a vertical cylindrical surface having a radius oand with its axis coincident with the Y axis. The non-parallel sides, each 01 length pi-po, are symmetrically disposed in planes perpendicular to the xz plane, forming with the XY plane a dihedral angle equal-to etc/2,. and

' parallel to the lines of electric intensity of the waves propagated within the horn. The horn is regarded as having a forward direction in the and bottom and the two side walls, respectively.

"I'huawe have the Hainfane the Ema types 0 waves.

For most applications of the hornfthe H waves are employed, particularly the two waves of lowest order, 110.1 and Hip. The reason for this choice is that the configuration of the field of these waves inside the horn is such as to produce positive direction of the x axis. The horizontal length of the mouth or aperture of the-horn is assumed to have a value b. and the corresponding length of the throat to have a value Do. The symbols illustrated in Fig. 4 have, therefore, the following meaning:

#0 represents the flare angle of the ,horn illustrated in Fig. 1; i

1) represents the horizontal dimension of the mouth or aperture oi this horn, or the distance between the opposite horizontally disposed sides of the horn, at the mouth 01' the horn;

a represents the corresponding vertical dimension, at right angles to the horizontal dimension, or the distance between the opposite vertically disposed'sideso! the horn, at the mouth of the horn. This vertical dimension is parallel to the lines 01 electric intensity of the waves propagated within the horn:

pi represents the radial length 01 the horn, meassubstantially single-lobelbeams of linear polarization in theradiated waves. Both waves have constant phase on cylindrical surfaces about'the axis within the horn.

. As before explained, it is an object of the present invention to designthe throat or the exciting means ll, or both, so that a desired wave, such as either-an Her orpHro wave, and also, in cases,

the desired wave only. shall exist in the horn, when used for transmitting; or so that the horn shall be responsive to the desired wave, such as either the Hai or H wave, or the desired wave alone, when used for receiving. a

The Ho,1 wave may be excited by the currentcarrying antenna rod It in the throat disposed parallel to the Y axis of Fig. 4, as shown in Fig. 2,

or by feeding an Ho,1 wave into the throat from the rectangular hollow pipe i8, as shown in Figs. 1 and 3.

The properties of the Ho,1 and the Hm waves will not be further described herein. A descripured along one of the flaring sides, from the I point or apex oi the horn tothe mouth or aperture: and

'po represents the cut-oil length, from the said apex to the free end of the throat of the horn.

These symbols will have approximately the sameor corresponding meanings in thecase of pyramidal horns two of the opposite sides of which may be more or less parallel. It is convenient to measure the lengths a, b, no and p1 in terms of the wave-length they may, therefore, if the same unit of length be used for all dimensions and for the wave-length A, be represented 1 by the symbols The space wave radiated by the horn in beams of diilerent configurations, and the response of .a receiving horn to waves arriving at diii'erent space angles, depends on the shape of the horn in all cross sections, and the configuration of the exciting system at the throat, or of the wave delivered there by'the hollow-pipe transmission line. It depends also on the. ilare angle ho 'and the cut-oil length o/A.

In general, there are two distinct groups of waves: E-waves, having a radial component of electric intensity. but no radial component of magnetic intensity, in the horn; and H-waves,-

having a radial component of magnetic intensity, but no radial component of ele'ctric intensity. in the'horn'. Two subscripts are needed to tion thereof may be round, for example, in-my copending application, Serial No. 249,005, filed January 3, 1939, which makes reference to a paper by L. J.'Chu and W. L. Barrow, entitled, "Electromagnetic waves in hollow metal tubes of rectangular crosssection, Proceedings of the Institute of Radio Engineers, vol. 26, No. 12, December, 1938, commencing at page 1520, a paper by W. L. Barrow, entitled, "Electromagnetic-horn radiators, Union Radio Scientifique International, N0. 79, p. 277, containing a revisionof a paper presented at the Joint Meeting 01' the said parallel to the Y axis. atright angles to the didefine thewaves of-diiierent=orders.--'1he sub- 75- rection oi propagation. It isof uniform intensity in the direction of the Y axis, but it has a halfsinusoidal distribution in intensity along arcs concentric with the Y axis, between the two flared sides, at right angles to the direction of propagation. The magnetic lines lie in planes perpendicular to the Y axis, or parallel to the XZ axis.

' The H1,o type of wave may be excited by the current-carrying antenna rod i4 disposed centrally inthe throat parallel to the XZ plane, as illustrated in Fig. 3, or by feeding an Hm wave into the throat froma rectangular hollow pipe.

In the H1,o wave, the electric lines of force lie along arcs concentric with the Y axis between the two flared sides; they have a uniform distribution along the arcs, but a half-sinusoidal distribution in the direction of the Y axis. lines lie in planes passing through the Y axis.

The magnetic for increasingly large flare angles o.

Analysis, verified by experiment,.. has demonstrated that the attenuation oi each wave is relatively large near theapex oi the horn it, which may be termed the attenuation region. but is progressively smaller at greater radial distances :from the apex, which may be termed the transmission region. The attenuation region obviously involves small values of p, and the transmission region large values of p, and the boundary between the two regions is not definite. The attenuation region extends from the apex outward over .progressively shorter portions of the horn For small flare angles o6, therefore, the attenuation region extends overlarge distances from the apex. As the flare angle 4:0 is increased, the attenuation region shrinks and is confined substantially to the throat. The radial distance, from the apex radially outward, to which the region 01 relatively higli attenuation extends, is progressively greater for waves 01' higher order than for waves of lower order.

Analysis, verified by experiment, has also established that there is a best position for the antenna rod ll, the horn It being carried back far enough toward the apex of the horn so as to at- I tenuate undesirable waves and to send forth only the desired waves. In a horn of a given flare which is high up. oil the scale of Fig. 5. The intensity of this K0,: wave will. therefore, be so small that the wave will be substantially suppressed. As the same applies, in an increasing degree, to waves of still higher order, the Hm wave wlllalone be permitted principally to reach the mouth of the horn. By so designing the throat oi the horn. therefore, this Hm wave may except when a is very large compared to A.

The above-described attenuation property 01' the horn provides for eflective elimination oithe angle 8c, and for a givenwave-length A, there- M fore, a particular value for the cut-ofilength pc from the apex of the horn to the exciting antenna It may be adopted that will permit the Hm wave to form and travel freelythrough the horn to be radiatedinto space from its mouth substantially tin-attenuated, but that will afiect almost complete attenuation or filtration of higher-order waves H Hos, etc. during propagation from the exciting antenna toward the mouth. Horns for the production of single-lobe smooth beams should have their cut-oil lengths po not too different from their optimum value. A proper value of pi to be associated with this optimum cut-oil length c-may be chosen in accordance with the design of application, Serial No. 249,005, abovementioned.

The relation between the flare angle gin and the optimum cut-01f length p0, measured in terms of the wave-length 7\, for the high-attenuation region, for the Ho,1 and the Has waves, is illustrated in Fig. 5. The vertical cylindrical surface coaxial with the Y axis and at a distance p therefrom represents the transition between re gions of high attenuation, near the apex of the horn, to the region of free transmission, towards the mouth, for waves of the Ho,1 type. This corresponds to the curve m=l. The corresponding curve for the Ho,a wave is indicated at m=3.

- For example, if the flare angle o is the exciting antenna II should be disposed approximately at adistance higher-order waves. Let it be assumed, as an example, that the horn is excited for the Ho,1 wave by a small antenna ll in its throat. As the current oscillates in the antenna l4, not only the Hm wave, but also the higher-order waves, or spatial harmonics, H0,m, are produced, which tend to propagate in the radial direction of the horn. In the vicinity of the throat of the horn, the field distribution, along an arc of the horn, is nonsinusoidal, because of the presence of these H0,m waves, and is so configured that the boundary conditions at the surface of the antenna H are satisfied. The magnitude of the fields of the higher-order waves are less than the magnitude of the field oi the Ho,: wave at the throat of the horn. For a given flare angle 50, the range of the attenuation region is approximately proportional to the order of the wave. If the throat of the horn is appropriately near the horn apex, it may be in the transmission region of. the Hat wave, but it may be deep in the attenuation region 0! the higher-order waves (m=3 Most of the energy 01' the Ho,1 wave, therefore, will be freely transmitted out through the horn, but only a a small fraction of the energy of the higherorder waves will travel as far as the mouth of the horn. The field distribution across the mouth of the horn, therefore, will be substantially free of the third and still higher-order waves; it will be shelf-period sinusoid.

This may be understood from Fig. 7, embodying a number of curves plotted with the absolute value of the electric intensity E in the plane oi.

. the mouth of the horn as the ordinate, and the distance from the center of the mouth in the horizontal direction, parallel to the Z coordinate,

In this position, the antenna l4 will, at the same time, be within the attenuation region for the higher-order wave Hon, which will sufler extremely high attenuation in traveling through the small part of the horn until a distance from'the apex is reached equal to measured in .centimeters, as the abscissa, for diflerent values of flare angle, o=20, 40, 60, .For o=20 and also for o=40, the distribution is substantially smooth and half-sinusoidal. For larger values of flare angle #10, however, small irregularities, that are barely noticeable for o=40, become more and more pronounced until, when o=60, the distribution assumes a jagged saw-tooth form. The curves of Fig. '7 clearly illustrate this transition from a sinusoidal distribution for small flare angles o to a non-sinusoidal distribution that contains higher harmonic components of space variation for large flare angles #10.

A corresponding series of radiation patterns, each in a plane substantially at right angles to the lines of electric intensity of the waves within the horn, and which may be found in Fig. 3 of the said Barrow paper in the Union Radio Scientific Internationale, show the effect of progressively increasing the flare angle u from o=0.

corresponding to an open-end hollow pip to a maximum value of o=90. were made at points ina circular path having a radius of 100 feet. The exciting antenna H was near the end of the hollow pipe ll, Fig. 1.

For o=l0, the radiated energy is formed into a rather broad beam 'along the principal axis, and there is an irregular back-radiation curve. As on is made larger, the beam becomes sharper up to a value of o=between 40 and 60. At both these angles the beam is quite sharp. As the flare angle is made even greater, the beam becomes distorted by the appearance of secondary lobes, which push out into the principal lobe, broadening the beam as shown in Fig. 3G. For o=90, the secondary lobes are nearly as large as the principal lobe and the beam has been spread into a fan-shaped pattern with almost uniform radiation over an 80 sector.

Particularly noteworthy is the shape of the pattern for flare angles of 40 to 60. There is only one lobe of small amplitude and the back radiation, which is of relatively small amplitude, is confined to a small angle. This unusually clean-cut pattern offers possibilities not easily obtained by other types of radiators. The practical absence of secondary lobes in the forward half-plane contrasts markedly-with the presence of two or more such lobes of objectionably large amplitude in the patterns of conventional arrays of half-wave antennas and of parabolic reflectors.

A comparison of these radiation patterns with Fig. 7 shows that a sinusoidal variation of electric intensity across the mouth of the horn corresponds to a radiation pattern having a single principal lobe and secondary lobes of insignificant amplitudes. Non-sinusoidai distributions, on the other hand, occuring with flare angles 4w greater than 60, correspond to irregular radiation patterns.

The irregular shape, involving the strong secondary lobes, may be attributed to the harmonic components of the distribution across the mouth of the horn. Even if the distribution had remained sinusoidal, however, there would have been a broadening of the main lobe for increasing fiare angles o greater than about 50, because, as the waves travel outward in the radial direction in the horn, a horn of large flare angle 4m can not concentrate the waves mainly in a single direction, even inside the horn.

The decrease in the width of the beam with increasing flare angle on up to o=about 50 may be attributed to the increase in the horizontal dimension b of the mouth or aperture of the horn. Further increase in fiare angle distorts the distribution across the mouth from the sinusoidal form, and causes actual widening of the beam and the appearance of secondary lobes.

' When radiation by means of the H1,o wave in sectoral or slightly pyramidal horns desired, similarly, the higher-order Hm, H5,o be eliminated or filtered. Unlike the case of the Hm wave just discussed, this wave is substantially independent of the flare angle of the horn, but has a sinusoidal variation in the vertical or Y direction. In the sectoral horn, the transmission properties of the Hap waves depend mainly upon the distance between the parallel, or top and bottom, surfaces of the horn. The attenua- The measurements,

' in this case, therefore, be achieved by adjusting r the vertical horn dimension a. The Hm wave will travel freely in the radial direction through the horn when a is greater than M2, but for free transmission of the Hat wave, a must be greater than 3M2, and soon for higher-order waves. To eliminate the higher-order waves, therefore, the dimension a should be slightly greater than M2, but less than 3M2. To eleminate the H2,o and Hi waves in the horn, the exciting system may be constructed with even symmetry about the waves should i tion is caused solely by decreasing the energy density as the area of the vertical cylindrical surface, coaxial with the Y axis, increases with horizontal plane equidistant between the two upper and lower sides of the horn, as viewed in Fig. 4.

The attenuation constant a may be defined as the logarithmic rate of decrease of magnitude in the direction of propagation, along the X axis,

in Fig. 4. The phase constant p may be defined I as the logarithmic change of phase along the said X axis. It is known that, for the H0,m wave,

J represents the Bessel function of the first w kind, and

represents the Bessel function of the second kind and the Neumann function, and K is the derivative of K with respect to the argument The attenuation constant 0:, of course, is the real part of this expression.

It may be shown that, for small values of p in the attenuation region, approximately,

and in the transmission region, for large values of p, approximately,

The attenuation region is that portion of the horn in which the phase constant p is very small compared to the value 21r/A for a wave in free space; and the transmission region is that portion of the horn in which the phase constant 6 is sub-v stantially equal to 21r/ Fig. 6 is a plot of curves, for the H0,m wave,

corresponding to horns of perfect conductivity, measured in terms of 0/01, where c is the velocity of light, and w=21rf, f being the frequency( The curves will be somewhat steeper in practical horns, but the nature of the curves is the same. The ordinate in these curves is the attenuation constant a, and the abscissa is stated, plotted in Fig. 5.

a measure of the radial distance p. The curves of Fig. 6 correspond to different values of from the lower transmission region, indicated by TR. This dotted-line boundary between these two regions, although indefinite, has been taken as the lowest root of The lowest-root solution of this equation yield o/A as a function of mar/m:

Two curves, for m=1 and m= 3, representing this cut-oif-frequency equation, are, as before will If this last equation be plotted, with Do and 41:0 as co-ordinates for diiferent values of m, it will be found that for m=l, corresponding to the H wave, Do/i is substantially equal to, but a little greater than which indicates that the exciting means l4-should be disposed in the horn in such a place that the horizontal length oi? the throat of the horn, or the transverse distance,

' Do, is not greatly less than M2, a half wavelength. It is also found from this expression that for m=3, corresponding to the Has wave, the value Do/i is substantially equal to, but. a little greater than 3/2. Therefore, if the exciting means I4 is positioned in the horn at a place where the transverse distance Do is as great as 3M2, the Ho,a wave may be strongly excited. These two conditions, taken together, show that the said transverse dimension Do, or the position of the exciting or absorbing mea'ns I4 in the horn, should be substantially equal to or slightly greater than M2 but not as great as 3M2. In fact, to obtain the greatest amount of attenuation for the H03 wave, which will result in its substantial elimination for small flare angles n, the transverse distance Do should be substantially equal to A/2.

More general y, to obtain the Ho,m wave and suppress the higher-order waves, the transverse dimension Do, or the position of the exciting or absorbing means M in the horn, should be substantially between of all waves of higher order. For the Hon wave,

should be positioned, or the hollow pipe I! should be connected to the horn l6, at the point deter-. mined by the equation approximately, or a little more or less. To pass the Hon wave, this distance should be approximately that is, the length of the horn will be at least long enough to pass substantially the Ho.: wave. The higher-order waves will thus stantially eliminated.

As an illustration, the curve for in Fig. 6, applies to the Hon wave in a horn having a flare angle n=60.

The analysis is not rigorous, and it is impossible, with present knowledge, to lay down rigorous rules or exact formulas. The formulas serve merely as a first approximation. Final adjustments must always be made, in practice, under conditions of actual operation. Variations of as much as fifty per cent, and even more, from the mathematical relations deduced theoretically, have been observed, in actual practice.

Though the description above has been specifically with respect to sectoral and slightly pyramidal shapes, the same results may be obtained with a reasonable degree of accuracy, such as is usable in most engineering applications, with horn shapes that resemble the sectoral or slightly pyramidal. For example, the rectangular cross-section of these shapes may be modified slightly to have round instead of square comers, or a more or less fiat or other cross-section of substantially the same shape, without altering materially the radiation pattern and the applidiameter at the throat, or where the energy-* for example, the exciting or absorbing means 14 7 cability of the design relations of these specifications. It is the intention of this disclosure and the appended claims to include such modifications of the invention within its scope.

In the case of conical horns, for example, the transverse dimension at the throat or the position of the energy-translating means should be substantially equal to or slightly greater than the critical transverse dimension of a hollow pipe of circular cross-section for the corresponding type of wave. In particular, in a horn of the above-described shape, for radiation with the lowest-order transversely polarized wave, Hi, the

translating means is positioned, should be sub- Similarly, for horns of other cross-sectional shape, the transverse dimension at the throat or at the position of the energy-translating means may be determined from the critical relation to! hollow-pipe waves in a hollow pipe of the same cross-section.

Modifications will occur to persons skilled in the art and all such are considered to fall within the scope and spirit of the invention.

What isclaimed is:

1. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of H0,m waves of wave-length A having a radial component of magnetic intensity but no radial component of electric intensity in the horn, where m is a positive integer, the horn being provided with a pair of oppositely disposed flaring also be subtherein of Hon waves of wave-length A having a radial component or magnetic intensity but no radial component of electric intensity in the horn, where m is a positive integer, the horn being provided with a pair oi oppositely disposed flaring sides substantially parallel, and a pair or oppositely disposed sides substantially normal, to the lines of electric intensity or the said waves within the horn, and exciting or absorbing means positioned in the throat or the horn where the transverse dimension or the throat, between the flaring sides or the horn, is substantially equal to or greater than substantially M2.

3. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein or H0,m waves of wave-length A having a radial component or magnetic intensity but no radial component of electric intensity in the horn,where m is a positive integer, the horn being provided with a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, the horn having a cut-oi! throat portion the transverse dimension of which, between the flaring sides or the horn, is substantially equal to or greater than substantially M2.

4. An electromagnetic. horn of substantially sectoral shape adapted for the propagation therein of the lowest order, Hm, waves oi! wavelength x having a radial component of magnetic intensity but no radial component of electric intensity in the horn, the horn being provided with a pair-oi oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity or the said waves within the horn, the horn having exciting or absorbing means positioned where the transverse dimension of the throat, between flaring sides of the horn,

is between substantially M2 and3x/2;

5. An electromagnetic nom of, substantially sectoral shape adapted for the propagation therein of the lowest order, Hon, waves of wave-length a having a radial component or magnetic intensity but no radial component of electric intensity in the horn, the horn being provided with a pair or oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, and exciting or absorbing means positioned in the throat of the horn where the transverse dimension of the throat, between the flaring sides of the horn, is between substantially M2 and 3M2.

6. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of the lowest order, H04, waves of wave-length A having a radial component of magnetic intensity but no radial component of electric intensity in the horn, the horn being provided with a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely dis posed sides substantially normal, to the lines of electric intensity of the said waves within the horn, the horn having a cut-oi! throat portion the transverse dimension oi, which, between the flaring sides or the horn, is between substantially M2 and 3M2. p

7. An electromagnetic horn of substantially sectoral shape adapted for the propagation there- 'in of Ham waves of wave-length A having a radial component or magnetic intensity but no radial component 01 electric intensity in the horn, where m. is a positive integer, the, horn being provided with a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines oi electric intensity or the said waves within the horn, the horn having exciting or absorbing means positioned where the transverse dimension of the throat, between the flaring sides of the horn, is between substantially mg and (m +2};-

8. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of Hum: waves or wave-length x having a radial component or magnetic intensity but no radial component of electric intensity in the horn, where m is a positive integer, the horn being provided with a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, and exciting or absorbing means positioned in the throat of the horn where the transverse dimension of the throat, between the flaring sides oi the horn, is between substantially A A m and (m+2) 9. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of Hmm waves of wave-length A having a radial component of magnetic intensity but no radial component of electric intensity in the horn, where m is a positive integer, the horn being provided with a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, the horn having a cut-oif throat portion the transverse dimension of which, between the flaring sides of the horn, is between substantially 10. An electromagnetic system having, in combination, an electromagnetic horn adapted for the propagation therein of waves of a predetermined wave-length and having a small throat end and a large mouth end, and means for producing waves of the said wave length of a predetermined order and excluding waves of higher order comprising absorbing or exciting means positioned in the throat where the transverse dimension of the throat is substantially equal to or only slightly greater than the critical transverse dimension of ahollow pipe that will pass waves 01' the said wave-length.

11. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of H0,m waves of wave-length x having a radial component of magnetic intensity but no radial component of electric intensity in the horn, where sectoral shape adapted for the propagation therei in of Hu,m waves of wave-length A having a radial component of magnetic intensity but no radial component of electric intensity in the horn, where m is a positive integer, the horn beingprovided with a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of thesaid waves withinthe horn, and exciting or absorbing means positioned in the throat of the horn where the transverse dimension of the throat, between the flaring sides of the horn, is greater than avalue within about fifty per cent of substantially A/2.

13. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of H0,m waves of wave-length A having a radial component of magnetic intensity but no radial component of electric intensity in the horn, where m is a positive integer, the horn being provided with a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, the horn having a cut-oil throat portion the transverse dimension of which, between the flaring sides of the horn, is greater than a value within about flfty per cent of substantially M2.

14. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of the lowest order, Hon, waves of'wave-length A having a radial component of magnetic intensity but no radial component of electric intensity in the horn, the horn'being provided with a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, the horn having exciting or absorbing means positioned where the transverse dimension of the I throat, between flaring sides of the horn, is within parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, the horn having a cut-ofi throat portion the transverse dimension of which, between the flaring sides of the horn, is-within about fifty per cent of a value between substantially M2 and 3M2.

17, An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of Ho,m waves of wave-length A having a radial component ofmagnetic intensity but no radial component 01 electric intensity in the horn, where m is a positiveinteger, the horn being provided witha pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the linesof electric intensity of the said waves within the horn, the horn having exciting or absorbing means positioned where the transverse dimension of the throat, between the flaring sides of the horn, is within about flfty per cent of a value 18. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of Ham waves of wave-length A having a radial component of magnetic intensity but no radial component of electric intensity in the horn, where m is a positive integer, the horn being provided with a pair ,of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, and exciting or absorbing means positioned in the throat of the horn where the transverse dimension of the throat, between the flaring sides of the horn, is within about fifty percent of a value between substantially A A L m and (m+2) I 19-. An electromagneticv horn of substantially sectoral shape adapted for the propagation therein of Htun waves of wave-length A having a radial 1 component of magnetic intensity but no radial in the throat of the horn where the transverse dimension of the throat, between the flaring sides of the horn, is within about fifty per cent of a value between substantially M2 and 3M2.

16. An electromagnetic horn of substantially sectoral shape adapted for the propagation therein of the lowest order, Ho,1, waves of wave-length A having a radial component of magnetic intensity but no radial component of electric intensity in the horn, the horn being provided with a pair of oppositely disposed flaring sides substantially component of electric intensity in the horn, where m is a positive integer, the horn being provided with-a pair of oppositely disposed flaring sides substantially parallel, and a pair of oppositely disposed sides substantially normal, to the lines of electric intensity of the said waves within the horn, the horn having a cut-oil throat portion the transverse dimension of which, between the flaring sides or the horn, is within about'flity per cent of a value between substantially the throat end and the transverse dimension of which is substantially equal to or only slightly greater than the critical transverse dimension of a hollow pipe that willpass waves of the said wave-length. 

